A parametrized set of explicit elements of $\Sha(E/\Q)[3]$
Number Theory
2023-01-10 v2
Abstract
In this paper, we give explicit equations for homogeneous spaces corresponding to a rational isogeny of degree . An explicit set of elliptic curves with elements of order in their Tate-Shafarevich group is constructed. Combining this gives explicit examples of plane cubics over that have a point everywhere locally, but not globally.
Cite
@article{arxiv.2102.11737,
title = {A parametrized set of explicit elements of $\Sha(E/\Q)[3]$},
author = {Steven R. Groen and Jaap Top},
journal= {arXiv preprint arXiv:2102.11737},
year = {2023}
}
Comments
Accepted version, 16 pages